The cyclic open-closed map, u-connections and R-matrices

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• Kai Hugtenburg (Edinburgh)
• Wednesday 01 February 2023, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

This talk will review progress on obtaining Gromov-Witten invariants from the Fukaya category. A crucial ingredient is showing that the cyclic open-closed map, which maps the cyclic homology of the Fukaya category of X to its S1-equivariant quantum cohomology, respects connections. Along the way we will encounter R-matrices, which were used in the Givental-Teleman classification of semisimple cohomological field theories, and allow one to determine higher genus Gromov-Witten invariants from genus 0 invariants. I will then present some evidence that this approach might extend beyond the semisimple case. Time permitting, I will also explain work in progress on obtaining open Gromov-Witten invariants from the Fukaya category.

This talk is part of the Differential Geometry and Topology Seminar series.

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